We re-examine attempts to study the many-body localization transition using measures that
are physically natural on the ergodic/quantum chaotic regime of the phase diagram. Using …

In contrast with Anderson localization where a genuine localization is observed in real
space, the many-body localization (MBL) problem is much less understood in Hilbert space …

The dynamical phase diagram of interacting disordered systems has seen substantial
revision over the past few years. Theory must now account for a large prethermal many-body …

The Anderson transition in random graphs has raised great interest, partly out of the hope
that its analogy with the many-body localization (MBL) transition might lead to a better …

The article reviews the physics of Anderson localization on random regular graphs (RRG)
and its connections to many-body localization (MBL) in disordered interacting systems …

In this paper we study the many-body localization (MBL) transition and relate it to the
eigenstate structure in the Fock space. Besides the standard entanglement and multifractal …

We perform a thorough and complete analysis of the Anderson localization transition on
several models of random graphs with regular and random connectivity. The unprecedented …

In this paper, we suggest an extension of the Rosenzweig-Porter (RP) model, the LN-RP
model, in which the off-diagonal matrix elements have a wide, log-normal distribution. We …

Dynamical and spatial correlations of eigenfunctions as well as energy level correlations in
the Anderson model on random regular graphs (RRG) are studied. We consider the critical …

Multifractal dimensions allow for characterizing the localization properties of states in
complex quantum systems. For ergodic states the finite-size versions of fractal dimensions …